UV Mapped a cube for a skybox, seams showing
UV's are used to define a link between a 3d surface and a 2d surface. When a colour is needed for the 3d surface it finds a location in 2d space and then chooses the nearest pixel from the image. While rounding floating point numbers and choosing the nearest pixel from the image there can be slight variations while following the edge between two points. While texture painting may get drawn to the left, the renderer may choose from the right.

For this reason it is common to bleed the texture colour past the visible edge of the UV's so that there is always a valid colour to be chosen. This means you need to leave some space between islands when laying out your UV's.

When texture painting there is an option to set the amount of bleed, it's location is probably a bit misleading as it is found within the project paint settings.